Injection mold assembly and method of designing same

ABSTRACT

An injection mold assembly for injection molding an object includes a first mold tool having a first tool surface and a second mold tool having a second tool surface. The first and the second tool surfaces are cooperatively configured to define a mold cavity between the tool surfaces for an injection molding of an object. The first mold tool has a tool element with a first side that has the first tool surface, and with a second side opposite the first side. Multiple fins extend from the second side of the tool element. A base supports the fins. The tool element, the fins and the base define a coolant flow cavity at the second side of the tool element. A method of designing the mold assembly is also disclosed.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a divisional application of U.S. application Ser.No. 14/180,657, filed Feb. 14, 2014, which is hereby incorporated byreference in its entirety.

TECHNICAL FIELD

The present teachings generally include an injection mold assembly and amethod of designing an injection mold assembly.

BACKGROUND

Injection molded components are typically molded in a mold cavity formedbetween a first mold tool and a second mold tool. The first mold tool issometimes referred to as the cavity side mold tool and the second moldtool is sometimes referred to as the core side mold tool. Plastic ismelted in the mold cavity, and must be sufficiently cooled prior toseparating the mold tools and ejecting the molded component. Cooling ofthe molded component is accomplished via a coolant, such as water,flowing through coolant lines drilled in the first and second moldtools. The mold tools are generally a relatively hard tool steel.Accordingly, the drilled passages are generally drilled as a series ofstraight segments. If the molded component has a complex or curved outersurface, the straight passages will not be an equal distance from thecomponent as the cooling passages traverse the tool, resulting in unevencooling of different portions of the tool surface. Cycle time formolding the component is thus dependent on those portions of the toolsurface furthest from the cooling passages, and is increased untilrequired cooling is achieved.

One known process, referred to as direct metal laser sintering, providesconformal cooling channels that can be equally spaced from the toolsurface to enable more even cooling. The conformal cooling channels areprovided by locally melting metal powder with a focused beam, layer bylayer. This process is expensive as it is relatively slow and requiresunique equipment and training that most mold makers do not have.

Additionally, the layout of the cooling channels is generally performedaccording to a trial and error, iterative process that relies on theskill level of the tool designer for each iterative layout of thecooling channels. Specifically, the designer selects an initial coolingchannel pattern and inputs the layout into a computer that implements atool design program that indicates the resulting tool surfacetemperature distribution. If the temperature distribution is notsatisfactory, the designer reconfigures the cooling channel layout basedon an educated guess, inputs the revised cooling channel layout into thecomputer, and the tool design program then determines whether thetemperature distribution is sufficiently improved. This process isrepeated however many times as necessary, is time consuming, andconsistently obtaining a satisfactory final result is somewhatuncertain, as this is generally dependent upon the skill of thedesigner.

SUMMARY

An injection mold assembly is provided that enables sufficiently uniformcooling of molded components with a reduced cycle time in comparison toprevious mold assembly cooling configurations. Additionally, the moldassembly can be designed with cooling channels positioned according toan automated method that satisfies requirements of a final coolingchannel layout by correlating mold tool surface temperature distributionand cooling channel properties, with each iteration of cooling channelpositions being driven by the previous mold tool surface temperaturedistribution and an optimization algorithm.

More specifically, an injection mold assembly for injection molding anobject includes a first mold tool having a first tool surface and asecond mold tool having a second tool surface. The first and the secondtool surfaces are cooperatively configured to define a mold cavitybetween the tool surfaces for injection molding of an object. The firstmold tool has a tool element with a first side that has the first toolsurface, and with a second side opposite the first side. Multiple finsextend from the second side of the tool element. A base supports thefins. The tool element, the fins and the base define a coolant flowcavity at the second side of the tool element such that coolant in thecoolant flow cavity contacts the second side of the tool element. Inother words, the entire second side of the tool element exposed betweenthe fins is in contact with coolant in the coolant flow cavity. The toolelement can be configured to have a substantially uniform thicknessbetween the first side and the second side, so that coolant in contactwith the second side is at a uniform spacing from the first toolsurface, minimizing cycle time and improving cooling uniformity. As usedherein a “substantially uniform thickness” is a thickness of the toolelement across the first tool surface that varies no more than apredetermined amount, such as an amount within the dimensionaltolerances of the formed tool element, or by no more than 5 to 10%pending the customer's needs.

A method of designing an injection mold assembly includes providing aninitial layout of a selected number of cooling channels. Each coolingchannel is modeled by a selected number of cooling elements. Eachcooling channel is in contact with and follows a contoured surface on acooled side of a mold tool element.

The method includes calculating temperatures of tool surface elements ofa tool surface on a tool surface side of the mold tool element that isopposite the cooled side. The tool surface elements spatially correspondwith the cooling elements and are cooled by coolant flow in the coolingchannels via heat conduction through the tool element. Under the method,it is determined whether a predetermined condition is satisfied by thecalculated temperatures of the tool surface elements. If thepredetermined condition is not satisfied, a revised layout of thecooling channels is generated according to an optimization module thatuses the calculated temperatures of the tool surface elements. Themethod iterates layouts of the cooling channels until the predeterminedcondition is satisfied. Specifically, calculating tool surface elementtemperatures corresponding with the cooling elements in the revisedcooling channel layout from the previous iteration, determining whetherthe predetermined condition is satisfied, and generating a revisedcooling layout is repeated until the predetermined condition issatisfied. The cooling channel layout that satisfies the predeterminedcondition is the final cooling channel layout. An injection moldassembly is then provided with the tool element and with coolingchannels and the cooled side that corresponds with the final coolingchannel layout.

The iteration process is automated, in that it is carried out by acomputer-implemented algorithm. The portion of the algorithm thatcalculates temperatures of the tool surface elements can be carried outby separate tool design software. By interfacing the tool designsoftware with the automated and optimized cooling channel iterations,tool design time is reduced and the resulting cooling channel layoutenables a more uniform tool surface temperature distribution.

The above features and advantages and other features and advantages ofthe present teachings are readily apparent from the following detaileddescription of the best modes for carrying out the present teachingswhen taken in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration in partial cross-sectional side viewof an injection mold assembly.

FIG. 2 is a schematic cross-sectional illustration of mold tools of themold assembly of FIG. 1. forming an object.

FIG. 3 is a schematic illustration in cross-sectional view taken atlines 3-3 of one of the mold tools of FIGS. 1 and 2.

FIG. 4 is a schematic illustration in cross-sectional view taken of analternative embodiment for the mold tools of FIG. 3.

FIG. 5 is a schematic illustration of a flow diagram of a method ofdesigning a mold assembly with tool elements and pillars as shown inFIG. 2.

FIG. 6 is a schematic illustration in perspective view of a portion ofone of the mold tools of FIG. 2 with an initial cooling channel layoutshown in phantom.

FIG. 7 is a schematic illustration in perspective view of a moldedobject that has been molded in the mold assembly of FIGS. 1 and 2.

FIG. 8 is a schematic illustration in cross-sectional view of the moldtool of FIG. 3 showing the initial cooling channel layout of FIG. 6 andcorresponding locations of pillars.

FIG. 9 is a schematic illustration in fragmentary side view of the toolelement of one of the mold tools of FIG. 2 and one of the coolingchannels of FIG. 8, showing representative tool elements and coolingelements.

FIG. 10 is a schematic illustration in schematic cross-sectional viewtaken at lines 10-10 in FIG. 8 of a portion of the mold element andpillars of FIG. 2.

DETAILED DESCRIPTION

Referring to the drawings, wherein like reference numbers refer to likecomponents, FIG. 1 shows an injection mold assembly 10 for injectionmolding an object 12, such as the complex contoured plastic object 12shown in FIG. 6. As further explained herein, the injection moldassembly utilizes novel mold tools 14, 16 that enable more uniformcooling of the object 12. Cooling flow paths through the mold tools 14,16 can be optimized according to an efficient design method.

The injection mold assembly 10 utilizes a motorized reciprocating screw18 that delivers molten plastic through a nozzle 20 into a mold cavity22 formed by and between the first mold tool 14 and the second mold tool16. Heaters 24 surround a barrel 26 that supports the screw 18 and meltthe plastic, which is fed into the barrel 26 from a plastic hopper 28 asplastic pellets 30. A motor 32 turns the screw 18, and a hydrauliccylinder 34 is controlled via an electronic controller 36 to reciprocatethe screw 18. The plastic is fed through a passage in a stationaryplaten 38 that supports the second mold tool 16, which is also referredto as the cavity tool. A movable platen 40 supports the first mold tool14, i.e., the core tool. A hydraulically-actuated clamping cylinder 42can also be controlled by the controller 36 to move the movable platen40 and the first mold tool 14 attached thereto to close the tools 14,16, after which time the plastic is injected into the cavity 22.Pressure is maintained by the cylinder 42, and a cooling system 44controlled by the controller 36 regulates the temperature of the moldtools 14, 16 as described herein. A pump 45 is used to circulate thecoolant through the cooling system 44. The cooling system 44 shownincludes a supply manifold that directs the coolant to the cavity 22,and a collection manifold that receives the coolant from the cavity 22and directs the coolant back through a temperature control device andthrough the pump 45. Once the object 12 (shown in FIG. 2) issufficiently formed and cooled, the clamping cylinder 42 is retracted,opening the cavity 22, and ejector pins (not shown), eject the moldedobject 12. It should be appreciated that, although only one controller36 is shown and described, multiple interconnected controllers could beused to control the various systems of the mold assembly 10.

FIG. 2 shows a portion of the mold assembly 10 in fragmentary view androtated 90 degrees relative to FIG. 1 for clarity. The first and secondmold tools 14, 16 are configured to be relatively inexpensive toproduce, yet enable uniform cooling of the tool surfaces in contact withthe object 12 while reducing cycle time in comparison to traditionalcooling arrangements. The first mold tool 14 has a tool element 46 thathas a first side 48 with a first tool surface 50 facing and partlydefining the mold cavity 22. The second mold tool 16 has a tool element63 with a second tool surface 52 facing and partly defining the moldcavity 22. The first and the second tool surfaces 50, 52 arecooperatively configured to define the mold cavity 22 between the toolsurfaces 50, 52.

The tool element 46 has a second side 54 opposite the first side 48 andalso referred to as the cooled side. Multiple fins 56 extending from thesecond side 54 of the tool element 46. A base 58 supports the fins 56.The fins 56 can also be referred to as pillars or stanchions, as eachacts as a structural support for the tool element 46 and must bearpressure loading during the molding process. In the embodiment shown,the fins 56 are integral with the first tool element 46. The toolelement 46, the fins 56 and the base 58 define a coolant flow cavity 60at the second side 54 of the tool element 46 such that coolant in thecoolant flow cavity 60 contacts the second side 54 of the tool element46 to cool the surface 55 of the second side 54. End members 59 extendfrom the tool element 46 to enclose the sides of the coolant flow cavity60. The end members 59 seal to the second tool element 63, describedbelow, at seals 61 to enclose the mold cavity 22. The tool element 46 isa tool steel sufficiently hard to withstand the pressures required forinjection molding. The tool element 46 can be machined so that a moldwall thickness (mwt) 62 of the tool element between the first side 48and the second side 54 remains within a predetermined range at leastover the entire first tool surface 50.

The second mold tool 16 also has a tool element 63 that has a first side64 with the second tool surface 52, and has a second side 66 oppositethe first side 64. Multiple fins 68 extend from the second side 66 ofthe tool element 63. The fins 68 can also be referred to as pillars orstanchions, as each acts as a structural support for the tool element 63and must bear pressure loading during the molding process. Each of thefins 56 has a different respective height H1, H2, H3, H4, H5 asnecessary to span the coolant flow cavity 60 from the complex, contouredtool element 46 to the base 58. A base 70 supports the fins 68. In theembodiment shown, the fins 68 are integral with the base 70. The toolelement 63, the fins 68 and the base 70 define another coolant flowcavity 72 at the second side 66 of the tool element 63 such that coolantin the coolant flow cavity 72 contacts and cools the surface at thesecond side 66 of the tool element 63. End members 71 extend from thebase 70 to enclose the sides of the coolant flow cavity 72. The toolelement 63 is a tool steel sufficiently hard to withstand the pressuresrequired for injection molding. The tool element 63 can be machined sothat a mold wall thickness (mwt) 74 of the tool element 63 between thefirst side 64 and the second side 66 remains within a predeterminedrange over at least the entire second tool surface 52. The base 70 andfins 68 can optionally be a less expensive material than the tool steelof the second tool element 63. For example, the base 70 and fins 68 canbe aluminum.

FIG. 3 shows a cross section of a portion of the tool 14 in which thefins 56 have been positioned and sized according to a method thatutilizes an optimization algorithm to provide a final layout of coolantflow paths 71A, 71B, 71C, 71D, 71E, and 71F through the coolant flowcavity 60. The final layout is optimized to satisfy a predeterminedcondition, such as a temperature distribution at the first tool surface50 in which all temperatures are substantially uniform, in that they areall within a predetermined range, or as further described herein.

FIG. 4 shows an alternative tool 14A that could be used in place of tool14 in FIG. 1. The tool 14A also has a coolant flow cavity 60A with anarrangement of the fins 56A positioned to provide coolant flow paths71G, 71H, 71I, 71J, 71K and 71L through the coolant flow cavity 60A thatachieves a temperature distribution at the first tool surface 50 inwhich all temperatures are substantially uniform, in that they are allwithin a predetermined range. The fins 56A each have an airfoil-shapedcross-section normal to their respective height H1, H2, H3, H4, H5 asshown in FIG. 4. The airfoil-shaped cross-section decreases resistanceto flow. The more angular, generally rectangular cross section of thefins 56, on the other hand, may locally increase turbulence through thecoolant flow paths. The fins 56A each have an outer surface 75 incontact with the cooling fluid in the coolant flow cavity 60A, and areeach oriented about a respective longitudinal axis 76 so that the outersurface 75 will direct the cooling fluid to promote the uniformtemperature distribution. In other words, some of the fins 56A arepositioned somewhat at an angle relative to general direction of flow 78to locally increase or decrease the cooling effect on the tool element46. As further explained herein, the cooling flow paths 71A, 71B, 71C,71D, 71E, and 71F are between adjacent ones of the fins 56 and havewidths configured so that tensile stress, shear stress, and deflectionof the tool 14 are below predetermined maximum limits

FIG. 5 is a flow diagram of a method 100 of designing an injection moldassembly such as the injection mold assembly 10 of FIG. 1. The method100 is described with respect to the first mold tool 14, including thetool element 46, fins 56, coolant flow cavity 60 and base 58. The method100 is equally applicable to the design of the second mold tool 16,including the tool element 63, fins 68, coolant flow cavity 72 and base70. In fact, each tool 14, 16 would be analyzed individually forsatisfaction of a predetermined condition, as discussed herein. Many ofthe blocks or steps of the method 100 can be configured as a singlealgorithm, stored on and executed by a single processor on a singlecomputer, or different portions of the method 100 can be separatealgorithms that interface with one another and are stored on andexecuted by a processor, or are stored on and executed by multipleprocessors that may be on a single computer or multiple computers.

The method 100 begins with block 110, providing an initial layout of apredetermined number of cooling channels representing cooling flow pathsthrough the cooling flow cavity 60 between adjacent sets of fins 56.There cooling channels 80 are cylindrical models of the actual coolingflow paths in cavity 60 or 72, which are open cavities interrupted onlyby the fins 56 or 68, as shown in FIGS. 2 and 8. However, the ability tosimplify modeling of the less constrained cooling flow paths usingphysical properties of coolant flowing in constrained cylindricalcooling channels enables the final positions and sizes of the fins 56 tobe determined.

The initial layout will be revised according to an iterative procedure,as described herein, to arrive at a final layout that satisfies apredetermined condition. For example, referring to FIG. 6, an initialmodel 46A of the tool element 46 is shown without the fins 56 that willestablish the coolant flow paths in the coolant flow cavity 60. Theinitial model 46A is shown from an underside so that the cooled surface55 of the second side 54 is visible. The initial layout includes anumber of cooling channels 80 that are representative of coolant flowpaths. Each cooling channel 80 is in contact with, normal to, andfollows the contoured cooled surface 55 of the second side 54 (i.e., thecooled side) of the tool element 46. The number of cooling channels 80selected can be derived from a cooling power estimation subroutine,based on approximate cooling time for the mold cycle to produce theobject 12, and based on an estimate of the total amount of heat to beremoved by the cooling system during the mold cycle. In other words, thenumber of cooling channels 80 selected is that needed to remove thenecessary heat in the desired cycle time.

Other system requirements or limitations can be imposed on the physicalcharacteristics or other parameters of the injection mold assembly 10 ormolding process in determining the final locations of the coolingelements 82 and corresponding dimensions of the tool elements 46, 63,and of the pillars 56, 68. For example, it may be desirable to minimizecooling time for manufacturing efficiency.

For example, the cooling time and number of cooling lines can beoptimized to maximize the heat transfer rate {dot over (Q)}_(conduction)from the mold while maintaining a uniform temperature at the toolsurface 50, 52; where:

${{\overset{.}{Q}}_{conduction} = {k\frac{\partial T}{\partial z}}};$

where k is the thermal conductivity of the tool elements 46, 63;

$\frac{\partial T}{\partial z}$

is the temperature gradient of the tool elements 46, 63 in the directionz of the thickness (i.e., the mold wall thickness mwt) of the toolelements 46, 63.

The temperature of the surfaces 50, 52 of the tool elements 46, 63 isrelated to time during the cooling cycle as flows:

${T_{x = 0}(t)} + \left( {{T_{coolant} + {\left( {T_{melt} - T_{coolant}} \right){\sum\limits_{m = 0}^{\infty}{\frac{\left( {- 1} \right)^{m}}{{2m} + 1}^{\frac{\pi^{2}{\alpha {({{2m} + 1})}}^{2}}{h^{2}}s}}}}};} \right.$

where T_(coolant) is the coolant temperature; T_(melt) is thetemperature of the plastic in the cavity 22; m is mass; α is thermaldiffusivity and h is part thickness.

The rate of change of the temperature of the surfaces 50, 52 of the toolelements 46, 63 is related to the properties of the material of the toolelements 46, 63 as follows:

${\frac{\partial T}{\partial t} = {\alpha \frac{\partial^{2}\overset{\_}{T}}{\partial z^{2}}}};$

where T is the temperature of the tool elements 46, 63 in the directionz of the thickness (i.e., the mold wall thickness mwt) of the toolelements 46, 63; and α is the thermal diffusivity of the material of themold tools 46, 63.

Specifically, to estimate cooling power and thus the number of coolingchannels 80 required for one of the tools 14, 16, the cooling time inT_(c) in seconds can first be approximated based on the relationship:

${{TC} = {2\frac{s}{{mm}^{2}}*{mwt}\mspace{14mu} {mm}^{2}}};$

where s is part thickness in millimeters (mm) (i.e., the thickness ofthe object 12); where mwt is the mold wall thickness in millimeters (mm)of tool element 46 or 63. The amount of heat to be removed and the rateof heat transfer per cooling channel 80 can be estimated as follows:

Q_(m) = m * C_(p)(T_(melt) − T_(eject));${{\overset{.}{Q}}_{c} = \frac{Q_{m}}{TC}};{and}$

${{\overset{.}{Q}}_{channel} = \frac{{\overset{.}{Q}}_{c}}{n}};$

where Q_(m) is the total amount of heat to be removed from the moltenplastic; m is the mass of the plastic in the mold cavity 22 and in anyrunner passage or passages in the mold tool 14 or 16 leading to the moldcavity 22; C_(p) is the coolant specific heat; T_(melt) is the meltingtemperature of the plastic; T_(eject) is the temperature of the moldedobject 12 when ejected from the mold cavity 22; {dot over (Q)}_(c) isthe rate of heat to be transferred per mold cycle; TC is the coolingtime; {dot over (Q)}_(channel) is the rate of heat transfer per coolingchannel 80 (i.e., cooling channel power in Joules per second or Watts);and n is the number of cooling channels 80.

The coolant flow rate V in each channel 80 can be estimated from thefollowing relationship:

ΔT_(coolant)={dot over (Q)}_(channel)/(V*ρ*C_(p)); where ΔT_(coolant) isthe increase in temperature of the coolant in a single pass through thecooling channel; and ρ is the coolant density. ΔT_(coolant) can be setto the allowable increase in coolant temperature per pass, such as butnot limited to a number from 0.1 to 1 C (degrees Celsius), and the aboverelationship can be solved for V. The coolant flow rate V can also belimited by a requirement that the coolant flow in the channels 80 isturbulent in order to maximize heat transfer. The Reynolds number Re isrelated to the coolant flow rate by the following relationship:

${R_{e} = \frac{\rho \; {VD}}{\mu}};$

where ρ is the coolant density; V is the coolant flow rate, alsoreferred to as coolant velocity; D is the diameter of the channelequivalent (i.e., the equivalent diameter of the channel 80 to a channelthat is cylindrical in cross section, assuming the channel 80 is anoncylindrical channel, which can be estimated by multiplying thediameter of the round channel by an equivalency or adjustment factor.

The Reynolds number Re can be limited to a value above 2,300, with 4,000being a typical number. Additionally, the pressure in the coolingchannel 80 must be a value less than the maximum capable by the pump 45used to circulate the coolant, and the coolant heat removal rate perchannel, {dot over (Q)}_(channel), must be greater than or equal to thecooling channel output, and the capability of the mold temperaturecontroller to sufficiently monitor temperature with the speed andaccuracy required should be confirmed. An optimizing algorithm can beused to optimize the coolant heat removal rate {dot over (Q)}_(channel)versus the coolant pumping energy expended by the pump 45.

The area of a cooling channel 80 can be approximated between a maximumvalue and a minimum value for a cylindrical channel, each of which canbe converted into a pattern area size equivalent, to match the area of aselected linked pattern, such a linked pattern 88 discussed herein. Themaximum and minimum values can be approximated as follows:

${D_{\max} = \frac{\left( {4*\rho*V} \right)}{\pi*\mu*4000}};$

where the Reynolds number is 4,000;

${D_{\min} = \sqrt{\frac{\rho*l*V^{2}}{10\; \pi*\Delta \; P}}};$

where l is the length of the cooling channel; and ΔP is the pressuredrop permitted in the cooling channel 80. D_(max) and D_(min) can eachbe converted into a pattern area size equivalent by multiplying by acorrection factor that can be developed based on testing.

The cooling from the tool surfaces 50, 52 is related to the maximumpressure on the surfaces exerted by the pressurized melted plastic inthe mold cavity 22:

${P_{\max \; {melt}} = {\frac{\sigma_{endurance}}{2.6} = {175\mspace{14mu} {MPa}}}};$

where σ_(endurance) is the endurance stress, which is the maximum stressthat can be exerted on the plastic material in the mold cavity 22.

The spacing of the cooling channels 80, referred to as the coolingpitch, can also be limited by a maximum variance in the heat flux acrossthe tool surface 50, 52 of the tool element 46, 63 according to thefollowing relationship:

${{\Delta \; {\overset{.}{Q}\lbrack\%\rbrack}} \cong \left( \frac{W_{line}}{H_{line}} \right)^{2.8\; l\; {n{(\frac{W_{line}}{H_{line}})}}}};$

where Δ{dot over (Q)}[%] is the maximum variance in the heat flux acrossthe tool surface 50, 52 of the tool element 46, 63; W_(line) is thewidth of the cooling channel 80, denoted by l in FIG. 10; H_(line) isthe height of the cooling channel 80 from the cooled surface 55 of thetool element 46 (or the cooled surface of the tool element 63), denotedby the fin height fh in FIG. 10.

Each cooling channel 80 is modeled by cooling elements 82. The coolingelements 82 represent the coolant in the coolant flow cavity 60, witheach cooling element 82 representing the coolant at a specific location,identifiable by specific Cartesian coordinates.

For purposes of mathematical computations carried out under the method100, each cooling element 82 is paired with a tool surface element 84.Each tool surface element 84 represents the first tool surface 50 at aspecific location, identifiable by a specific Cartesian coordinate. Eachcooling element 82 is paired with a specific tool surface element 84directly opposite the specific cooling element 82 according to a linenormal to the thickness (mwt) 74 of the tool element 46 at the coolingelement 82. This is indicated in FIG. 9 with cooling elements denoted82A, 82B, 82C, 82D, and 82E paired with tool surface elements 84A, 84B,84C, 84D, and 84E, respectively. The tool surface elements 84A, 84B,84C, 84D, and 84E spatially correspond with the cooling elements 82A,82B, 82C, 82D, and 82E and are cooled by coolant flow in the coolingchannels 80 via heat conduction through the tool element 46.

Under the method 100, the number of cooling elements 82 per coolingchannel 80 to be used for purposes of the heat balance and transferequations utilized in the method 100 must be selected by the designer atthe outset of the design process. Although only five cooling elements82A, 82B, 82C, 82D, and 82E are shown for the cooling channel 80 in FIG.9, many more cooling elements would likely be selected for greateraccuracy in the modeling of heat transfer and other physicalcharacteristics of the tool element 14, fins 56, and coolant flow.Additionally, the cooling elements 82A, 82B, 82C, 82D, and 82E need notbe immediately adjacent one another as show in in FIG. 9, and caninstead be spread further apart from one another along the length of thecooling channel 80 of FIG. 6. Different numbers of cooling elements 82can be used to model different cooling channels 80 in the method 100, orthe same number can be used to model each channel 80.

FIG. 10 shows a cooling element 82 midway in the cooling channel 80between the tool element 46 and the base 58, to indicate that thephysical characteristics of each cooling element 82A, 82B, 82C, 82D, and82E shown in contact with the cooled surface 55 is actually based on theaverage of the coolant in the cooling channel 80 normal to the specificlocation on the cooled surface 55. References herein to cooling element82 also refer to the more specifically denoted cooling elements 82A,82B, 82C, 82D, and 82E. References herein to tool surface element 84also refer to the more specifically denoted tool surface elements 84A,84B, 84C, 84D, and 84E.

The specific location of each cooling element 82 will change as thelayout of the cooling channels 80 is revised during iterations ofportions of the method 100 until the desired predetermined condition issatisfied, as described herein. In one embodiment, the desiredpredetermined condition is satisfied when the temperatures of each ofthe tool surface elements 84 are determined to be within a predeterminedrange of temperatures. Alternatively, in another embodiment, thepredetermined condition is a predetermined number of iterations ofcalculating temperatures of the tool surface elements 84 in block 112,as described herein. Accordingly, in such an embodiment, the finallayout of the cooling channels 80, and the corresponding positions ofthe fins 56, is realized after the predetermined number of iterationshas been accomplished, such as by way of nonlimiting example, 50iterations. Although the cooling channels 80 are initially modeled asstraight, the final locations of the cooling elements 82 initiallyincluded in each initially straight cooling channel 80 will establish acooling flow path through the mold cavity 22 that will likely not becompletely straight, as indicated in FIGS. 3 and 4.

FIG. 8 shows an example of the initial layout of cooling channels 80input initially into the computer that executes the method 100, and theassociated initial positions of the fins 56. Each cooling channel 80 isbetween adjacent rows of fins 56, except the cooling channels at the farends, which are between an end member 59 and a row of fins 56. Variousdesign constraints can be implemented to govern the relationship betweenthe physical dimensions of the fins 56 and the cooling channel 80 bothin the initial layout and as limitations on changes to the layout duringthe automated iterative process. For example, the following designconstraints are implemented in providing the initial cooling channellayout. First, the ratio of fin separation (fg) to fin length (cfl)shown in FIG. 8 can be constrained as follows:

fg/cfl=0.5 to 0.1.

The range of allowable ratio of fin separation (fg) to fin thickness(ft) can be constrained as follows:

1.0<fg/ft>4.0.

The ratio of fin thickness (ft) to width (cc) of the cooling channel 80,also indicated as l, can be constrained as follows:

ft/cc<0.1.

The cooling channel 80 can be constrained so that the Reynolds number(Re) in the cooling channel 80 is above 2,300. Finally, the tool bitsize used in machining angled interfaces of the tool element 46 and thefins 56 can be constrained to a tool bit size with a radius of greaterthan 2 millimeters to result in a radius (r) of the interfaces, shown inFIG. 10, of greater than 2 millimeter.

Optionally, certain subsets of the cooling elements 82 can be linkedtogether in the design iterations so that revised locations of thelinked cooling elements 82 in each iteration maintain the same initialrelative placement to one another. Referring to FIG. 8, a tripletpattern of linked cooling elements, referred to as a linked pattern 88,may be used. For example, cooling elements 82 falling within the boundsof the linked pattern 88, surrounding a triplet pattern of fins 56, canbe manipulated to remain in the same relative location to one anotherthroughout the iterations.

The injection mold assembly 10 can also be optimized for one or more ofthe following: minimize cooling time, provide a heat flow balance inwhich the coolant heat flow in the cavities 60, 72 is equal to the heatflow of the plastic melt in the mold cavity 22, provide a coolant flowrate that minimizes a temperature differential across the tool elements46 and 63 and enables cooling channel efficiency, provides a pattern forthe cooling elements 82 that ensures turbulent flow (e.g., Reynoldsnumber greater than 2,300), provides final positions of the coolingelements 82 that provide uniform heat flow through the tool elements 46,63, ensures adequate tool life based on a cyclical stress failure curve,a pressure map of pressure applied to the tools 14, 16, and the numberof cycles the injection mold assembly 10 will be utilized, and ensuresthat a pressure drop across each cooling channel 80 would be enabled bya capability of the outside the tool ancillary heat extraction process.

For example, the heat flux from the plastic melt in the mold cavity 22can be determined by the algorithm in block 110 according to thefollowing relationships:

${Q_{m} = {\frac{\left( {\Delta \; h*A_{m}*s*p} \right)}{2}*{tc}}};$tc = TC + Tn; and TC = C_(C) * S²;

where Q_(m) is the total heat from the injected plastic melt for moldingthe object 12; Δh is the enthalpy difference in kilojoules per kilogram(kj/kg) of the specific enthalpy at the material temperature atinjection less the specific enthalpy at the material temperature atejection; p is the density of the plastic melt; A_(m) is the surfacearea of the molded object 12; TC is the cooling time during which themold tools 14, 16 are closed together with the injected plastic therein;Tn is the nonproductive time required for opening and closing the moldtools 14, 16 and the time for ejecting the molded object 12 from themold tools 14, 16; tc is the overall cycle time; S is the wall thicknessof the molded object 12; C_(C) is a cooling constant (with a range of 2to 3 seconds/mm²) that is physically similar for unfilledthermoplastics, and is used as a simple correlation for estimatingcooling time. C_(C) is an estimation of the cooling gradient in thecenter of the plastic. Graphs of cooling gradient versus Fourier numberare readily available to estimate geometry.

The cooling time TC is also related to the properties of the plasticmaterial of the molded object 12 as follows:

${{TC} = {\left( \frac{S^{2}}{a_{{eff}*\pi^{2}}} \right)*{\ln\left( {\frac{\frac{8}{\pi^{2}}\left( {{Tm} - {Tw}} \right)}{Te} - {Tw}} \right)}}};$${a = \frac{k}{\left( {p*{Cplas}} \right)}};$${{Fo} = \frac{\left( {a*t} \right)}{x^{2}}};$

where α is thermal diffusivity; α_(eff) is effective thermaldiffusivity; k is the thermal conductivity of the plastic material;Cplas is the specific heat of the plastic material; Fo is Fourier numberas determined from correlation charts between plates, cylinders, andother different geometries; Tm is the melting temperature of the plasticmaterial; Tw is the wall temperature of the mold cavity 22, which is thesame as the temperature of the tool surface 50; Te is the demoldingtemperature, also referred to as the temperature of the object 12 at thetime of ejection from the cavity mold 22. Notably, the S wall thicknessof the molded object 12 is a squared term in the cooling timerelationship above. Reducing the thickness of the object 12, thereforecan significantly reduce the cooling time. Cooling that utilizes themold tools 14, 16 enables very uniform cooling, which should allow areduced thickness in the molded object 12, and a related reduction inthe cooling time.

At equilibrium, {dot over (Q)}_(m)+{dot over (Q)}_(w)=0; where {dot over(Q)}_(m) is heat flux from the injected plastic melt for molding theobject 12; {dot over (Q)}_(w) is the heat flux into the tool element 46.The cavity wall temperature Tw at equilibrium can be solved if coolingtime TC is known. Cooling time TC can be an input to the system, or canbe estimated. Similarly, if the cavity wall temperature is Tw is known,the cooling time TC at equilibrium can be determined from the aboverelationship. In that case, the cavity wall temperature is Tw can be aninput to the system, such as if a certain cavity wall temperature TC isdesired.

The heat flow rate {dot over (Q)} for the coolant is related to the theparameters of a cooling system modeled by the cooling channels 80 asfollows:

${\overset{.}{Q} = {U*A*{Lc}*\left( {{Tc} - {Tf}} \right)}};$${U = \frac{{Nu}*K*12}{D}};$${{Nu} = {0.116*{{\Pr^{0.33}\left( {{Re}^{0.66} - 125} \right)}\left\lbrack {1 + {\left( \frac{D}{12*{Lc}} \right)0.66}} \right\rbrack}\left( \frac{\mu \; c}{\mu \; f} \right)^{0.14}}};$${\Pr = \frac{3600*c_{\rho}*\mu \; f}{K}};$

where Re is the Reynolds number of the coolant flow; Pr is the Prandtlnumber of the coolant flow; Nu is the Nusselt number of the coolantflow; Lc is the length of the cooling channel 80 in mm; D is thediameter of the cooling channel equivalent (i.e., the diameter of acylindrical channel equivalent in flow volume to the cooling channel 80with width l and height fh shown in FIG. 10); ρ is the coolant density;μ is the coolant fluid viscosity; μc is the coolant viscosity at thetemperature of the cavity 22; K is the coolant thermal conductivity; Cpis the coolant specific heat; Tc is the surface cavity temp; Tf is thecoolant temperature; A is the exposed surface cooling area at the side54; U is the heat transfer coefficient of the coolant; and {dot over(Q)} is the heat flow rate of the coolant.

The dimensions of the cooling channels 80 and the fins 56 or 68 can bebased an optimization of structural loading to ensure tool life (i.e.,integrity of the tools 14, 16). One optimization procedure is to selectthe cooling channel distance cc, also shown as l, based so that tensilestress, shear stress, and deflection of the tool elements 46, 63 remainbelow the maximum allowable tensile stress, the maximum allowable shearstress, and the maximum deflection of the tool elements 46, 63,respectively. For example,

${\sigma_{bmax} = \frac{0.5*P*l^{2}}{d^{2}}};$${\tau_{\max} = \frac{0.75*P*l}{d}};{and}$${f_{\max} = {\frac{1000*P*l^{2}}{d}*\left( {\frac{{Pl}^{2}}{32*E*d^{2}} + \frac{0.15}{G}} \right)}};$

where P is the pressure of the plastic in the mold cavity 22 acting onthe surfaces 50, 52 of the tool elements 46, 63; d is the depth of thetool element 46 or 63 in the z direction (i.e., the mold wall thicknessmwt); l is the width of the cooling channel 80 indicated in FIG. 10 andalso indicated as cc in FIG. 8; E is the tensile modulus in N/mm² ofeach of the fins 56 or 68; G is the shear modulus in N/mm² of each ofthe fins 56 or 68; σ_(bmax) is the allowable tensile stress of each ofthe fins 56 or 68; τ_(max) is the allowable shear stress in N/mm² ofeach of the fins 56 or 68; and f_(max) is the maximum allowed deflectionof the tool elements 46, 63.

Following block 110, the method 100 proceeds to block 112, in whichtemperatures are calculated for the tool surface elements 84A, 84B, 84C,84D, and 84E corresponding with the cooling elements 82A, 82B, 82C, 82D,and 82E. It should be appreciated that only tool surface elements 84A,84B, 84C, 84D, and 84E and corresponding cooling elements 82A, 82B, 82C,82D, and 82E for a portion of one cooling channel 80 are illustrated inFIG. 9, the calculated temperature distribution in block 112 is based on, the remaining blocks of the method 100 are carried out with respect toall tool surface elements 84 and all cooling elements 82 of all of thecooling channels 80 simultaneously. Block 110 may be carried outaccording to various steady state conduction equations described hereinto provide a mold surface temperature distribution. The calculation ofthe temperature distribution in block 112 may be according to a tooldesign program that interfaces one or more other programs that carry outportions of the method 100, such as to provide cooling element locationiterations as described herein. The injection pressure distribution ofthe injected plastic in the mold cavity 22 on the surfaces 50, 52 of thetool elements 46, 63 would be provided as an input to the tool designprogram prior to the temperature distribution calculation in block 112.Any suitable programming language can be used for interfacing thecalculation of temperatures in block 112 based on the cooling elements(and therefore cooling channel) layouts, which can be accomplished by acomputer aided engineering mold flow software program, block 114(integration controller), and block 118, generating revised coolingelement locations by solving an optimization algorithm.

Based on the temperature distribution of the tool surface elements 84provided in block 112, the method 100 then proceeds to block 114 todetermine whether the predetermined condition is satisfied. If thepredetermined condition is simply performing block 112 a predeterminednumber of times, then the determination in block 112 can be made by asimple counting function included in the algorithm. However thepredetermined condition may be satisfying a requirement that thetemperatures of all of the tool surface elements 84 calculated in block112 are within a predetermined range of a target temperature, which maybe referred to as a convergence condition. The target temperature may be10 degrees Celsius to 300 degrees Celsius depending on the applicationand resin used in the plastic material. The temperatures of the toolsurface elements 84 are determined from the heat flow relationshipsdescribed herein between the molded plastic material, the tool element46, and the coolant flow. There may be additional requirements for theconvergence condition, such as that the calculated temperatures of allof the tool surface elements 84 of the tool element 46 may also berequired to be within 5 degrees Celsius of one another. Additionally,the convergence condition may also require that the temperatures of allof the tool surface elements 84 of the tool element 63 must also bewithin 5 degrees Celsius of one another when the second mold tool 16 isseparately analyzed under the method 100. When both of theserequirements for the tool element 46 and the tool element 63 are met,satisfaction of the convergence condition may also require that thedifference in the average temperature of the tool element 46 and thetool element 63 must not be more than 20 degrees Celsius.

If the predetermined condition is satisfied in block 114, then locationsof the cooling elements 82 are optimized, and the method 100 moves toblock 116 in which a tool element 46 and pillars 56 corresponding withthe cooling element positions is provided. A tool element 63corresponding with cooling element 82 positions following the analysisof the coolant flow cavity 72 is also provided. As discussed herein,optimization of other factors affecting the final dimensions determinedfor the tool elements 46, 63 and pillars 56, 68 can also be consideredand reflected in the heat flow calculations undertaken in determiningthe temperature distribution of tool surface elements 84 and resultingpositions of the cooling elements 82. By way of non-limiting example,the dimensions of the tool elements 46, 63, and of the pillars 56, 68can also be optimized for one or more of the following: to minimizecooling time, provide a heat flow balance in which the coolant heat flowin the coolant flow cavities 60, 72 is equal to the heat flow of theplastic melt in the mold cavity 22, to provide a coolant flow rate thatminimizes a temperature differential across the tool elements 46 and 63and enables cooling channel efficiency, to provide a pattern for thecooling elements 82 that ensures turbulent flow (e.g., Reynolds numbergreater than 2,300), to provide final positions of the cooling elements82 that provide uniform heat flow through the tool elements 46, 63, toensure adequate tool life based on (i) a cyclical stress failure curve,(ii) a pressure map of pressure applied to the tools 14, 16, and (iii)the number of cycles the injection mold assembly 10 will be utilized,and to ensure that a pressure drop across each cooling channel 80 wouldbe enabled by a capable external heat extraction process.

If the predetermined condition is not satisfied in block 114, then themethod 100 instead moves to block 118 in which a revised layout of thecooling elements 82, and hence the cooling channels 80, is generatedaccording to an optimization algorithm that uses the calculatedtemperatures of the tool surface elements 84 from block 112. In otherwords, the Cartesian coordinates of each of the cooling elements 82 inthe revised layout is based on the temperature distribution of the toolsurface elements 84.

A scalar field F is generated for the tool surface elements 84 andcooling elements 82 in the region of the tool element 46 or 63 that isin contact with the plastic in the mold cavity 22, and another scalarfield is generated for the tool surface elements 84 and the coolingelements 82 in the region of the tool element 46 or 63 that is not incontact with the plastic in the mold cavity 22. The value for each ofthe tool surface elements 84 and cooling elements 82 is expressed as ascalar function:

F=F(x, y, z), where x, y, z are the Cartesian coordinates.

The scalar fields drive the moving of the cooling elements 82 in eachiteration, as Laplacian operation for Laplacian F=0 is performed foreach of the regions of the tool element 46 and 63 (i.e., the region incontact with the plastic and the region not in contact with theplastic). Each Laplacian operator is given by a sum of secondderivatives of the function with respect to each independent variable asdescribed herein. The movement of each cooling element 82 from itslocation (Cartesian coordinates) in the previous layout to its newlocation in the succeeding revised layout is defined by the gradient ofthe scalar function:

v=−∇F, where v is the moving vector for the local mold region. Forexample, the optimization algorithm for steady state heat conductionbegins with the overall heat transfer governed by the three-dimensionalPoisson equation:

${\rho \; C_{p}\frac{\partial T}{\partial t}} = {k\left( {\frac{\partial^{2}T}{\partial x^{2}} + \frac{\partial^{2}T}{\partial y^{2}} + \frac{\partial^{2}T}{\partial z^{2}}} \right)}$

for r∈Ω; where T is the temperature of the tool surface element 84 atthe x,y,z Cartesian coordinate; t is time; ρ is the density of plastic;C_(p) is the specific heat of plastic; r radius and Ω is the domain. Forthe steady state LaPlace equation then:

${k_{m}\left( {\frac{\partial^{2}\overset{\_}{T}}{\partial x^{2}} + \frac{\partial^{2}\overset{\_}{T}}{\partial y^{2}} + \frac{\partial^{2}\overset{\_}{T}}{\partial z^{2}}} \right)} = 0$

for r∈Ω_(m); where k_(m) is mean thermal conductivity and T is the cycleaverage mold temperature (i.e., the average temperature of the plasticin the mold cavity 22 during the molding time of the object 12, notincluding the opening and closing time of the mold tools 14, 16).Accordingly, the steady state LaPlace equation provides the gradient, orthe direction of movement, for each cooling element 82 from one coolingchannel layout to the next iterative cooling channel layout. With thedirection of movement known for each cooling element 82, any one of manystandard potential optimization algorithms can then be used to determinethe next sets of Cartesian coordinates for the cooling elements 82, witheach cooling element 82 moving in a direction in accordance with thegradient determined from the solution of the steady state LaPlaceequation. The LaPlacian will be positive if concave and negative ifconvex. The results will be compared to the average. This will directthe sequential optimization. Other standard optimization methods may beused for approximation or for certain subroutines, prior to using theLaPlacian, such as the kriging method or the Monte Carlo method. Thesemay be used along with Design of Experiments (DOE) methods or samplingtechniques such as full factorial, D-optimal design, central compositedesign, orthogonal array, and Latin hypercube.

As discussed herein with respect to FIG. 8, groups of adjacent coolingelements 82 can be linked in a pattern, such as a triplet linked pattern88 of cooling elements 82. Other patterns of linked cooling elements 82can instead be used. The use of a linked pattern of cooling elements isbeneficial because it avoids strong gradients or large changes betweenadjacent cooling elements. For example, the system can apply a rule suchthat features of adjacent elements do not vary by more than 10 percent.

Thus, after block 118, in which each cooling element 82 is movedaccording to the results of the vector field generated from the scalarfield and the selected optimization algorithm, the method 100 returns toblock 112, and the revised cooling element locations (making up thecorresponding revised cooling channels 80) are provided as inputs toblock 112, the portion of the algorithm that calculates temperatures ofthe tool surface elements 84 corresponding with the new cooling elementlocations (i.e., normal to each cooling element location and at thesurface of the tool element 46 or 63).

The recalculated surface temperature profile in block 112 is thenevaluated in block 114 to determine whether the predetermined conditionis satisfied. Blocks 112, 114, and 118 are repeated until thepredetermined condition is satisfied. When the predetermined conditionis satisfied, the final positions of the cooling elements 82 are known,and the corresponding positions and dimensions of the pillars 56, 68 aretherefore known. The method 100 thus moves from block 114 to block 116,in which the mold tools 14, 16 with the tool elements and pillars 56, 68are manufactured and provided as discussed above.

While the best modes for carrying out the many aspects of the presentteachings have been described in detail, those familiar with the art towhich these teachings relate will recognize various alternative aspectsfor practicing the present teachings that are within the scope of theappended claims.

1. A method of designing an injection mold assembly comprising:providing an initial layout of a predetermined number of coolingchannels representing cooling flow paths; wherein each cooling channelis modeled by a selected number of cooling elements; wherein eachcooling channel is in contact with and follows a contoured surface on acooled side of a mold tool element; calculating temperatures of toolsurface elements of a tool surface on a tool surface side of the moldtool element opposite the cooled side; wherein the tool surface elementsspatially correspond with the cooling elements and are cooled by coolantflow in the cooling channels via heat conduction through the toolelement; determining whether a predetermined condition is satisfied bythe calculated temperatures of the tool surface elements; generating arevised layout of the cooling channels according to an optimizationalgorithm that uses the calculated temperatures of the tool surfaceelements when the predetermined condition is not satisfied; repeatingsaid calculating, determining, and generating until the predeterminedcondition is satisfied; and manufacturing the tool element and fins thatdefine a cooling cavity at the cooled side having coolant flow pathscorresponding to the cooling channels of the revised layout in which thepredetermined condition is satisfied.
 2. The method of claim 1, whereineach tool surface element is positioned on the tool surface normal to arespective different one of the cooling elements.
 3. The method of claim1, wherein the temperatures are calculated based on steady state heatconduction through the tool element.
 4. The method of claim 1, whereinthe revised layout of the cooling channels is established byrepositioning the cooling elements such that a pattern of adjacent onesof the cooling elements is maintained.
 5. The method of claim 1, whereinthe predetermined condition is the temperature of all of said toolsurface elements being within predetermined range of temperatures. 6.The method of claim 1, wherein the predetermined condition is apredetermined number of iterations of said calculating temperatures. 7.The method of claim 1, wherein the optimization algorithm is based on atleast one of temperature distribution of the tool surface elements,minimization of cooling cycle time, balancing of heat flow from plasticat the cavity side to coolant at the cooling side, minimizing atemperature change in each of the cooling channels, maintainingturbulent flow through the cooling channels, maintaining uniform heatflow through the tool element, avoiding cyclical stress failure of thetool assembly, and pressure drop in each of the cooling channels.
 8. Themethod of claim 1, wherein the fins are connected to and extend from thesecond side of the tool element; wherein a base supports the fins;wherein the tool element, the fins and the base define the coolant flowcavity at the second side of the tool element; wherein the tool elementis configured to have a substantially uniform thickness between thefirst tool surface and the coolant flow cavity; and wherein the fins arepositioned to establish the coolant flow paths in the coolant flowcavity, each of the coolant flow paths being between adjacent ones ofthe fins; and further comprising: configuring widths of each of thecooling channels between adjacent ones of the fins so that the fins aresized to ensure that tensile stress, shear stress, and deflection of thetool element are below predetermined maximum limits.